Communications in Analysis and Geometry

Volume 26 (2018)

Number 4

Bishop and Laplacian comparison theorems on Sasakian manifolds

Pages: 915 – 954

DOI: https://dx.doi.org/10.4310/CAG.2018.v26.n4.a8

Authors

Paul W. Y. Lee (Chinese University of Hong Kong, Shatin, Hong Kong)

Chengbo Li (Department of Mathematics, Tianjin University, Tianjin, China)

Abstract

We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for a natural sub-Riemannian structure defined on Sasakian manifolds. This generalizes to arbitrary dimensions the corresponding three-dimensional results in [1, 5, 6].

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The first author’s research was supported by the Research Grant Council of Hong Kong (RGC Ref. No. CUHK404512).

The second author was supported in part by the National Natural Science Foundation of China (Grant No. 11201330).

Received 18 November 2013

Published 6 September 2018